Creating Random Points Problem

I am just trying to create random sampling points along roads. The points can't be within 1 Km of each other. The random sampling point tool allows you to set the minimum allowed distance between points. However, I think this tool only counts distance between each point along the same line. It doesn't count the distance from roads that are parallel or perpendicular to the point. (See image) I do have the line data dissolved.

Does anyone know how to get this to work. keep in mind I work for the govment and I can't just download and install other free extensions or tools.